Alexandre Cabot, Hans Engler, Sebastien Gadat
We investigate the asymptotic properties as of the differential equation
where is -valued, the map is non increasing, and is a potential with locally Lipschitz continuous derivative. We identify conditions on the function that guarantee or exclude the convergence of solutions of this problem to points in , in the case where is convex and is an interval. The condition
is known to be necessary for convergence of trajectories. We give a slightly stronger condition that is sufficient.
Published April 15, 2009.
Math Subject Classifications: 34G20, 34A12, 34D05.
Key Words: Differential equation; dissipative dynamical system; vanishing damping; asymptotic behavior.
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| Alexandre Cabot |
Département de Mathématiques, Université Montpellier II, CC 051
Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
| Hans Engler |
Department of Mathematics, Georgetown University Box 571233
Washington, DC 20057, USA
| Sébastien Gadat |
Institut de Mathématiques de Toulouse, Université Paul Sabatier
118, Route de Narbonne 31062 Toulouse Cedex 9, France
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